This sounds like an add on interacting with the functionality of the url bar or malware. First try safe mode: Diagnose Firefox issues using Troubleshoot Mode

Sometimes a problem with Firefox may be a result of malware installed on your computer, that you may not be aware of.

You can try these free programs to scan for malware, which work with your existing antivirus software:

• Microsoft Safety Scanner
• MalwareBytes' Anti-Malware
• Anti-Rootkit Utility - TDSSKiller
• AdwCleaner (for more info, see this alternate AdwCleaner download page)
• Hitman Pro
• ESET Online Scanner

Microsoft Security Essentials is a good permanent antivirus for Windows 7/Vista/XP if you don't already have one. Windows 8 has antivirus built-in already.

Further information can be found in the Troubleshoot Firefox issues caused by malware article.

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Maybe it's this: Due to a change in how Firefox 39 associates keywords with bookmarks and/or history, the address bar is newly sensitive to corruption in the database that stores your history and bookmarks (the places.sqlite file).

The developers are working on a solution, but that could take weeks to get to you.

At this point, the easiest workaround is to remove/rename the places.sqlite file, but then you lose all your history, so that's really not very attractive for people who rely on history for revisiting sites.

In case you want to try that (in case you don't receive any better suggestions), here's how:

Open your current Firefox settings (AKA Firefox profile) folder using either

• "3-bar" menu button > "?" button > Troubleshooting Information
• (menu bar) Help > Troubleshooting Information

In the first table on the page, click the "Show Folder" button. This should launch a new window listing various files and folders in Windows Explorer.

Leaving that window open, switch back to Firefox and Exit, either:

• "3-bar" menu button > "power" button
• (menu bar) File > Exit

Pause while Firefox finishes its cleanup, then rename places.sqlite to something like oldplaces.sqlite. (I suggest not deleting this file just in case you end up needing it again.)

Firefox creates temporary files related to places.sqlite and those may need to be renamed/removed as well. Check for places.sqlite-shm and places.sqlite-wal and if you find them, rename them as well.

When you start Firefox back up again, it should start a new places.sqlite database and import your last automatic bookmark backup. Can you confirm that all your bookmarks are present? Does the address bar work normally again?